# Problems on Profit Loss

Q21. A company offers three types of successive discounts. 1st 20% and 10% ; 2nd 15% and 15%, 3rd 25 % and 5%. Which offer is better for a customer ?

(a) 1st

(b) 2nd

(c) 3rd

(d) All are equal

**Answer:** (c) 3rd

Let the M.P be Rs. 100

1st payment = 80% of 90% of Rs. 100

= | 80 | X | 90 | X 100 |

100 | 100 |

= Rs. 72

2nd payment = 85% of 85% of Rs. 100

= | 85 | X | 85 | X 100 |

100 | 100 |

= Rs. 72.25

3rd payment = 75% of 95% of Rs. 100

= | 75 | X | 95 | X 100 |

100 | 100 |

= Rs. 71.25

∴ 3rd payment is better

Q22. A discount series of P% and Q% on an invoice is the same as a single discount of

(a) (p - q + | pq | )% |

100 |

(b) {(p + q) - | pq | }% |

100 |

(c) [100 - (p + q + | pq | )]% |

100 |

(d) [100 - (p - q + | pq | )]% |

100 |

**Answer:**

(b) {(p + q) - | pq | }% |

100 |

Let the M.P be Rs. 100, then

S.P = (100 - p)% of (100 - q)% of Rs. 100

= Rs. { | 100 - p | X | 100 - q | X 100 } = Rs. | (100 - p) (100 - q) |

100 | 100 | 100 |

Single discount = { 100 - | (100 - p) (100 - q) | } % |

100 |

= [ | 1000 - { 1000 - 100q - 100p + pq} | ] % |

100 |

= | 100q + 100p - pq |

100 |

= { (p + q) - | pq | }% |

100 |

Q23. A retailer allows a trade discount of 10% on the cost. By how much above the cost should the product be labelled for sale to gain 18%.

(a) 31%

(b) 31(1/9)%

(c) 35%

(d) 35(1/3)%

**Answer:** (b) 31(1/9)%

Let the C.P be Rs. 100 and let the M.P be Rs. x above Rs. 100

Then M.P = Rs. (100+x) and discount = 10%

∴ S.P = | 90 | X (100 + x) = Rs. | 9 (100 + x) |

100 | 10 |

∴ | 9 (100 + x) | = 118 |

10 |

⇒ 100 + x = | 118 X 10 |

9 |

∴ x = | 1180 | - 100 |

9 |

= | 1180 - 900 | = | 280 |

9 |

= 31 | 1 | % |

9 |

∴ Cost should be labelled at 31(1/9)% above C.P

Q24. A shopkeeper gives two sucessive discounts on an article marked Rs. 600. The first discount given is 10%. If the customer pays Rs. 459 for the article, the second discount given is

(a) 10%

(b) 12%

(c) 13%

(d) 15%

**Answer:** (d) 15%

Let the second discount be x%

∴ 90% of (100 - x)% of Rs. 600 = Rs. 459

⇒ | 90 | X | 100 - x | X 600 = 459 |

100 | 100 |

⇒ | 27 (100 -x) | = 459 |

5 |

⇒ 100 - x = | 459 X 5 |

27 |

⇒ 100 - x = 85

⇒ x = 100 - 85 = 15 %

Q25. A shopkeeper sold an air-conditioner for Rs. 25938 with a discount of 10% and earned a profit of 4%. What would have been the percentage of profit earned if no discount were offered.

(a) 13.21%

(b) 15.55%

(c) 17.20%

(d) 22.85%

**Answer:** (b) 15.55%

Let the M.P be Rs. x

∴ x X (90/100) = 25938

⇒ x = (25938 X 10)/9 = 28820

∴ M.P = Rs. 28820

S.P = Rs. 25938

Profit = 4%

∴ C.P = (100/104) X 25938 = Rs. 24940.38

New S.P = Rs. 28820

C.P = Rs. 24940.38

∴ Profit = Rs (28820 - 24940.38) = Rs. 3879.62

Profit % = (3879.62/24940.38) X 100 = 15.55%

Q26. A trader marks his goods at such a price that he can deduct 10% for cash and yet make 20% profit. The marked price of an item which cost him Rs. 90.

(a) Rs. 120

(b) Rs. 130

(c) Rs. 135

(d) Rs. 145

**Answer:** (a) Rs. 120

C.P = Rs. 90

Gain % = 20%

S.P = Rs. (120/100) X 90 = Rs. 108

Let M.P be Rs. x

Now 90% of x = 108

⇒ (90/100) X x = 108

⇒ x = (10800/90) = 120

∴ M.P = Rs. 120

Q27. A dealer buys an article marked at Rs. 24000 with 20% and 5% off. He spends Rs. 1000 on its repairs and sells it for Rs. 24000. What is his gain or loss percent ?

(a) 18.15 %

(b) 22.31 %

(c) 24.74 %

(d) 29.25 %

**Answer:** (c) 24.74 %

C.P = {80% of 95% of Rs. 24000} + 1000

= | 80 | X | 95 | X 24000 + 1000 |

100 | 100 |

= Rs. (18240 + 1000)

= Rs. 19240

S.P = Rs. 24000

∴ Profit = Rs. (24000 - 19240) = Rs. 4760

∴ Profit % = (4760 / 19240) X 100 = 24.74 %

Q28. An article is listed at Rs. 800 and two successive discounts of 8% and 8% are given on it. How much would the seller gain or loss, if he gives a single discount of 16% instead of two dicounts ?

(a) Rs. 5.12

(b) Rs. 6.50

(c) Rs. 11.25

(d) Rs. 15

**Answer:** (a) Rs. 5.12

In 1st case

S.P = 92% of 92% of Rs. 800

= | 92 | X | 92 | X 800 |

100 | 100 |

= Rs. 677.12

In 2nd case,

S.P = 84% of Rs. 800

= (84/100) X 800

= Rs. 672

Loss = Rs. (677.12 - 672) = Rs. 5.12

Q29. A tradesman gives 4% discount on the marked price and gives 1 article free for buying every 15 articles and thus gains 35%. The marked price is increased above the cost price by

(a) 29%

(b) 37%

(c) 42%

(d) 50%

**Answer:** (d) 50%

Let, the C.P of each article be Rs. x

C.P of 16 article be Rs. 16x

S.P of 15 articles = 135% of Rs. 16x

= Rs. (135/100) X 16x = Rs. (108x/5)

S.P of 1 article = Rs. ( | 108x | X | 1 | ) = Rs. | 36x |

5 | 15 | 25 |

If S.P is Rs. 96, M.P = Rs. 100

S.P is Rs. (36x/25), M.P = Rs. ( | 100 | X | 36x | ) = Rs. | 3x |

96 | 25 | 2 |

Increase in M.P over C.P = Rs. ( | x | X | 1 | X 100 )% = 50% |

2 | x |

Q30. A trader wishes to gain 20% after allowing 10% discount on the marked price to his customers. At what percent higher than the cost price must he mark his goods ?

(a) 19(1/3)%

(b) 26(1/4)%

(c) 27(1/4)%

(d) 33(1/3)%

**Answer:** (d) 33(1/3)%

Let, the C.P be Rs. 100

Let the M.P be Rs. x above Rs. 100

∴ S.P = Rs. [ | 90 | X (100 + x)] = Rs. [ | 9 (100 + x) | ] |

100 | 10 |

∴ | 9(100 + x) | = 120 |

10 |

⇒ 9 (100 + x) = 1200

⇒ 9x = 1200 - 900

⇒ x = (300 / 9) = 33 (1/3)

∴ Cost should be labelled at 33(1/3)% higher than C.P